Question

Tìm:

a) \(\int x^4dx;\)                  b) \(\int\dfrac{1}{x^3}dx;\)                  c) \(\int\sqrt{x}dx\left(x>0\right).\)

Answer 1

a) \(\int {{x^4}dx}  = \frac{{{x^{4 + 1}}}}{{4 + 1}} + C = \frac{{{x^5}}}{5} + C\).

b) \(\int {\frac{1}{{{x^3}}}dx}  = \int {{x^{ - 3}}dx = \frac{{{x^{ - 3 + 1}}}}{{ - 3 + 1}} + C = \frac{{{x^{ - 2}}}}{{ - 2}} + C =  - \frac{1}{{2{x^2}}} + C} \).

c) \(\int {\sqrt x dx}  = \int {{x^{\frac{1}{2}}}dx}  = \frac{{{x^{\frac{1}{2} + 1}}}}{{\frac{1}{2} + 1}} + C = \frac{{{x^{\frac{3}{2}}}}}{{\frac{3}{2}}} + C = \frac{2}{3}\sqrt {{x^3}}  + C\).